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Paper version warnings incorrect

According to the book, valid keys are 1-2, 3-4, 5-6, 7-8, 4-1, 2-3, 6-7, 8-5, 2-5, 6-1, 4-7, and 3-8. The current warning heuristic is incorrect for some of these (e.g. 1-6 is valid, 3-6 is invalid).

A concise test for whether a key (i,j) is valid is

((i-1)>>1 ^ (j-1)>>1) < 3

Explanation:

  • (i-1)>>1 converts both the even and odd keys to [0,3]
  • a ^ b < 3 tests that the edit distance between pairs is 0 or 1 (since the numbers are 2-bit)

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